Analysis of Theoretical and Numerical Properties of Sequential Convex Programming for Continuous-Time Optimal Control
This work addresses a theoretical gap for researchers and practitioners in optimal control, though it is incremental as it builds on existing SCP methods.
The paper tackles the limited theoretical analysis of Sequential Convex Programming (SCP) for continuous-time optimal control by providing a unifying theoretical framework, deriving convergence guarantees, and offering practical insights for handling manifold constraints and accelerating methods.
Sequential Convex Programming (SCP) has recently gained significant popularity as an effective method for solving optimal control problems and has been successfully applied in several different domains. However, the theoretical analysis of SCP has received comparatively limited attention, and it is often restricted to discrete-time formulations. In this paper, we present a unifying theoretical analysis of a fairly general class of SCP procedures for continuous-time optimal control problems. In addition to the derivation of convergence guarantees in a continuous-time setting, our analysis reveals two new numerical and practical insights. First, we show how one can more easily account for manifold-type constraints, which are a defining feature of optimal control of mechanical systems. Second, we show how our theoretical analysis can be leveraged to accelerate SCP-based optimal control methods by infusing techniques from indirect optimal control.